1. Return and Risk The Capital Asset Pricing Model (CAPM)

2. Key Concepts and Skills
Know how to calculate expected returns
Know how to calculate covariances, correlations, and betas
Understand the impact of diversification
Understand the systematic risk principle
Understand the security market line
Understand the risk-return tradeoff
Be able to use the Capital Asset Pricing Model

3. Chapter Outline 10.1 Individual Securities
10.2 Expected Return, Variance, and Covariance
10.3 The Return and Risk for Portfolios
10.4 The Efficient Set for Two Assets
10.5 The Efficient Set for Many Assets
10.6 Diversification: An Example
10.7 Riskless Borrowing and Lending
10.8 Market Equilibrium
10.9 Relationship between Risk and Expected Return (CAPM)

4. 10.1 Individual Securities
The characteristics of individual securities that are of interest are the:
Expected Return
Variance and Standard Deviation
Covariance and Correlation (to another security or index)

5. 10.2 Expected Return, Variance, and Covariance
Consider the following two risky asset world. There is a 1/3 chance of each state of the economy, and the only assets are a stock fund and a bond fund.

6. Expected Return

7. Expected Return

8. Variance

9. Variance

10. Standard Deviation

11. Covariance
Deviation compares return in each state to the expected return.
Weighted takes the product of the deviations multiplied by the probability of that state.

12. Correlation

13. 10.3 The Return and Risk for Portfolios
Note that stocks have a higher expected return than bonds and higher risk. Let us turn now to the risk-return tradeoff of a portfolio that is 50% invested in bonds and 50% invested in stocks.

14. Portfolios
The rate of return on the portfolio is a weighted average of the returns on the stocks and bonds in the portfolio:

15. Portfolios
The expected rate of return on the portfolio is a weighted average of the expected returns on the securities in the portfolio.
Or, alternatively,
9% = 1/3 (5% + 9.5% %)

16. Portfolios
The variance of the rate of return on the two risky assets portfolio is
Note that variance (and standard deviation) is NOT a weighted average. The variance can also be calculated in the same way as it was for the individual securities.
where BS is the correlation coefficient between the returns on the stock and bond funds.

17. Portfolios Observe the decrease in risk that diversification offers.
An equally weighted portfolio (50% in stocks and 50% in bonds) has less risk than either stocks or bonds held in isolation.

18. 10.4 The Efficient Set for Two Assets
100% stocks
100% bonds
We can consider other portfolio weights besides 50% in stocks and 50% in bonds …

19. The Efficient Set for Two Assets
100% stocks
100% bonds
Note that some portfolios are “better” than others. They have higher returns for the same level of risk or less.

20. Portfolios with Various Correlations
return
100% stocks
 = -1.0
 = 1.0
 = 0.2
100% bonds 
Relationship depends on correlation coefficient
-1.0 < r < +1.0
If r = +1.0, no risk reduction is possible
If r = –1.0, complete risk reduction is possible

21. 10.5 The Efficient Set for Many Securities
return
Individual Assets P
Consider a world with many risky assets; we can still identify the opportunity set of risk-return combinations of various portfolios.

22. The Efficient Set for Many Securities
return
efficient frontier
minimum variance portfolio
Individual Assets P
The section of the opportunity set above the minimum variance portfolio is the efficient frontier.

23. Diversification and Portfolio Risk
Diversification can substantially reduce the variability of returns without an equivalent reduction in expected returns.
This reduction in risk arises because worse than expected returns from one asset are offset by better than expected returns from another.
However, there is a minimum level of risk that cannot be diversified away, and that is the systematic portion.

24. Portfolio Risk and Number of Stocks
In a large portfolio the variance terms are effectively diversified away, but the covariance terms are not. 
Diversifiable Risk; Nonsystematic Risk; Firm Specific Risk; Unique Risk
Portfolio risk
Nondiversifiable risk; Systematic Risk; Market Risk n

25. Systematic Risk Risk factors that affect a large number of assets
Also known as non-diversifiable risk or market risk
Includes such things as changes in GDP, inflation, interest rates, etc.

26. Unsystematic (Diversifiable) Risk
Risk factors that affect a limited number of assets
Also known as unique risk and asset-specific risk
Includes such things as labor strikes, part shortages, etc.
The risk that can be eliminated by combining assets into a portfolio
If we hold only one asset, or assets in the same industry, then we are exposing ourselves to risk that we could diversify away.

27. Total Risk Total risk = systematic risk + unsystematic risk
The standard deviation of returns is a measure of total risk.
For well-diversified portfolios, unsystematic risk is very small.
Consequently, the total risk for a diversified portfolio is essentially equivalent to the systematic risk.

28. Optimal Portfolio with a Risk-Free Asset
return
100% stocks rf
100% bonds 
In addition to stocks and bonds, consider a world that also has risk-free securities like T-bills.

29. 10.7 Riskless Borrowing and Lending
CML
return
100% stocks
Balanced fund rf
100% bonds 
Now investors can allocate their money across the T-bills and a balanced mutual fund.

30. Riskless Borrowing and Lending
CML
return
efficient frontier rf P
With a risk-free asset available and the efficient frontier identified, we choose the capital allocation line with the steepest slope.

31. 10.8 Market Equilibrium
return
CML
efficient frontier M rf P
With the capital allocation line identified, all investors choose a point along the line—some combination of the risk-free asset and the market portfolio M. In a world with homogeneous expectations, M is the same for all investors.

32. Market Equilibrium
CML
return
100% stocks
Balanced fund rf
100% bonds 
Where the investor chooses along the Capital Market Line depends on his risk tolerance. The big point is that all investors have the same CML.

33. Risk When Holding the Market Portfolio
Researchers have shown that the best measure of the risk of a security in a large portfolio is the beta (b)of the security.
Beta measures the responsiveness of a security to movements in the market portfolio (i.e., systematic risk).

34. Estimating b with Regression
Characteristic Line
Security Returns
Slope = bi
Return on market %
Ri = a i + biRm + ei

35. The Formula for Beta
Clearly, your estimate of beta will depend upon your choice of a proxy for the market portfolio.

36. 10.9 Relationship between Risk and Expected Return (CAPM)
Expected Return on the Market:
Expected return on an individual security:
Market Risk Premium
This applies to individual securities held within well-diversified portfolios.

37. Expected Return on a Security
This formula is called the Capital Asset Pricing Model (CAPM):
Expected return on a security =
Risk-free rate +
Beta of the security ×
Market risk premium
Assume bi = 0, then the expected return is RF.
Assume bi = 1, then

38. Relationship Between Risk & Return
Expected return b
1.0

39. Relationship Between Risk & Return
Expected return b
1.5

40. Quick Quiz
How do you compute the expected return and standard deviation for an individual asset? For a portfolio?
What is the difference between systematic and unsystematic risk?
What type of risk is relevant for determining the expected return?
Consider an asset with a beta of 1.2, a risk-free rate of 5%, and a market return of 13%.
What is the expected return on the asset?
Expected return = (8) = 14.6%